Question: Multiply the following complex numbers: $({2-i}) \cdot ({2-3i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({2-i}) \cdot ({2-3i}) = $ $ ({2} \cdot {2}) + ({2} \cdot {-3}i) + ({-1}i \cdot {2}) + ({-1}i \cdot {-3}i) $ Then simplify the terms: $ (4) + (-6i) + (-2i) + (3 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 4 + (-6 - 2)i + 3i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 4 + (-6 - 2)i - 3 $ The result is simplified: $ (4 - 3) + (-8i) = 1-8i $